1. Bundling vs. Separate Pricing

In this scenario, bundling coffee and bananas can be more profitable than selling separately. Here’s why:

• Price Discrimination Challenge: Since the cafe owner can’t distinguish between the two customer types, they can’t charge different prices for coffee and bananas individually. “Students with Early Classes” value the bundle more (coffee: $0.70 + banana: $0.50 = $1.20) than “Students without Early Classes” (coffee: $0.60 + banana: $1.00 = $1.60). Separate pricing would lose out on this opportunity.
• Exploiting Surplus Value: By bundling, the cafe owner can create a package that captures some of the surplus value (willingness to pay above marginal cost) of “Students without Early Classes” for bananas. This increases overall profit.

Bundle Price:

To determine the optimal bundle price, consider the following:

• Minimum acceptable price for each customer type:
  • “Students with Early Classes”: combined marginal cost (coffee: $0.10 + banana: $0.40) = $0.50
  • “Students without Early Classes”: their minimum acceptable price for the bundle (to avoid buying separately) is likely lower than $1.60 (their separate value), but higher than $0.50 (combined marginal cost).
• Profit maximization: The price should be as high as possible while still attracting both customer types.

Considering these points, a bundle price between $0.80 and $1.20 might be optimal. This captures some surplus value from “Students without Early Classes” while remaining attractive to “Students with Early Classes.”

2. Labor Negotiation Game
3. Diagram:

This is a simultaneous-move game where Management and Labor decide independently whether to hire a lawyer (L) or not (N). Here’s the payoff matrix:

drive_spreadsheetExport to Sheets

1. Nash Equilibrium:

The Nash equilibrium is where each side chooses the strategy that maximizes their payoff given the other side’s choice.

• For Management:
  • If Labor hires a lawyer (L), Management should also hire one (L) to avoid losing most of the time (0.75 vs 0.25).
  • If Labor doesn’t hire a lawyer (N), Management is indifferent between hiring (0.5) or not (0.5). However, since hiring a lawyer is a cost, not hiring (N) might be a slightly better option.
• For Labor (similar logic):
  • If Management hires a lawyer (L), Labor should also hire one (L) to avoid losing most of the time (0.25 vs 0.75).
  • If Management doesn’t hire a lawyer (N), Labor might be indifferent between hiring (0.75) or not (0.5). However, with the lawyer cost, not hiring (N) might be slightly better.

Therefore, the Nash equilibrium is where both sides choose not to hire a lawyer (N, N). This is because in both scenarios where one side hires and the other doesn’t, the benefit gained is less than the cost of the lawyer ($400,000).

1. Banning Lawyers?

Both sides might consider banning lawyers for a few reasons:

• Cost savings: Each side would save $400,000 every year.
• Focus on negotiation: Without lawyers influencing the proposals, the focus might shift towards genuine negotiation and compromise.

However, there are also potential drawbacks:

• Information asymmetry: Lawyers might help prepare more compelling proposals, even if slightly slanted. Without them, one side might be at a disadvantage if less skilled at negotiation.
• Escalation of conflict: Without the “threat” of a lawyer-prepared proposal, negotiations might become more confrontational.

Ultimately, the decision to ban lawyers depends on the specific priorities of management and labor. If cost savings and a focus on direct negotiation are more important, a ban might be considered. However, if information asymmetry and maintaining a professional negotiation style are crucial, keeping lawyers might be preferred.